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Probability Theory, Statistics and Exploratory Data Analysis
Week 2
Random variables and geometric series

QuizQuiz • 10 min10 minutes

Random variables and geometric series

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Due DateJun 1, 2:59 AM EDTJune 1, 2:59 AM EDT

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Random variables and geometric series

Graded Quiz • 10 min

Due Jun 1, 2:59 AM EDT

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Random variables and geometric series

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1.

Question 1

Consider random variable $X$ which distribution is defined in the following way. Variable $X$ can take any non-negative integer value and $P(X=k)=1/2^{k+2}$ for any $k>0$ . Find $P(X=0)$ . Enter proper fraction.

1 / 1 point

\frac{3}{4}

3/4

Correct

2.

Question 2

Consider the following random variable $Y$ . It takes only values of the form $1/2^k$ for positive integer $k$ and $P(Y=1/2^k)=1/2^k$ for each $k$ . Find expected value of this random variable. Enter answer as a proper fraction.

1 / 1 point

\frac{1}{3}

1/3

Correct